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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 322 · 40 questions
TalentJR

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

NameDateTime takenScore ___ / 40
  1. 1.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 70 (c) 79 (d) 80
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 16 (b) 5 (c) 17 (d) 15
  3. 3.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 442 (c) 546 (d) 555
  4. 4.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 552 (c) 440 (d) 553
  5. 5.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 513 (c) 523 (d) 522
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 17 (b) 7 (c) 18 (d) 19
  7. 7.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  8. 8.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 45 (c) 15 (d) 48
  9. 9.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 70 (c) 78 (d) 69
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 20 (d) 18
  11. 11.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 526 (c) 422 (d) 525
  12. 12.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 14 (c) 42 (d) 45
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 16 (b) 4 (c) 14 (d) 15
  14. 14.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 20 (c) 180 (d) 60
  15. 15.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  17. 17.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 240 (c) 232 (d) 241
  18. 18.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 69 (c) 23 (d) 72
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 2 (b) 3 (c) 5 (d) 4
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 7 (b) 17 (c) 19 (d) 18
  21. 21.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 21 (c) 7 (d) 63
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 9 (d) 21
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 18 (b) 6 (c) 17 (d) 16
  24. 24.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 1 (d) 3
  26. 26.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 99 (c) 36 (d) 33
  27. 27.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 494 (b) 633 (c) 624 (d) 634
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 3 (b) 5 (c) 4 (d) 6
  29. 29.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 90 (c) 33 (d) 10
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 16 (b) 15 (c) 5 (d) 17
  31. 31.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 54 (c) 6 (d) 21
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 15 (b) 14 (c) 4 (d) 16
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 14 (b) 3 (c) 15 (d) 13
  34. 34.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  35. 35.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 427 (c) 356 (d) 426
  36. 36.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 164 (c) 173 (d) 182
  37. 37.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 39 (c) 12 (d) 36
  38. 38.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 17 (b) 6 (c) 16 (d) 18
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 2 (b) 3 (c) 4 (d) 5

Answer key

  1. 79
  2. 16
  3. 555
  4. 552
  5. 522
  6. 18
  7. 4
  8. 45
  9. 69
  10. 19
  11. 525
  12. 42
  13. 15
  14. 60
  15. 5
  16. 3
  17. 240
  18. 69
  19. 4
  20. 18
  21. 21
  22. 20
  23. 17
  24. 2
  25. 3
  26. 33
  27. 633
  28. 5
  29. 30
  30. 16
  31. 18
  32. 15
  33. 14
  34. 7
  35. 426
  36. 173
  37. 36
  38. 8
  39. 17
  40. 4

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